Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, k, m
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _m_domain, _phase, _t

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(Qmult(NumBra(m, _t), InverseFourierTransform(_t), ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t))), InSet(k, _m_domain))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(k \mapsto \left\{{_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 45 body: 3
2	ExprTuple	45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11, 12
8	Literal
9	ExprTuple	45, 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operand: 47
12	Operation	operator: 18 operands: 19
13	Operation	operator: 20 operands: 21
14	Literal
15	ExprTuple	22, 47
16	Literal
17	ExprTuple	47
18	Literal
19	ExprTuple	23, 24
20	Literal
21	ExprTuple	25, 26
22	Variable
23	Operation	operator: 38 operands: 27
24	Operation	operator: 28 operands: 29
25	Literal
26	Operation	operator: 30 operands: 31
27	ExprTuple	32, 33
28	Literal
29	ExprTuple	45, 47
30	Literal
31	ExprTuple	34, 35
32	Literal
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 40 operand: 48
36	Literal
37	ExprTuple	46, 42, 43, 44, 45
38	Literal
39	ExprTuple	46, 47
40	Literal
41	ExprTuple	48
42	Literal
43	Literal
44	Literal
45	Variable
46	Literal
47	Literal
48	Literal